Formulae

Problem Solving
Rearranging
Subject of formula
Substitution
Examples of application
  • Maths
  • Other Subjects
Direct Proportion

Key Objectives (Year 8)
  • Use formulae from mathematics and other subjects
  • Substitute integers into simple formulae, including examples that lead to an equation to solve
  • Substitute positive integers into expressions involving small powers, e.g. 3x2 + 4 or 2x3
  • Derive algabraic expressions and formulae

Delivery Ideas

Remember key vocabulary:
algebraic expression, equation, formula, partition, multiply out, cubed, square root, to the power of…

Show how algebra can be useful in real life.

Make clear the difference between an expression and an equation.

Use letter symbols in different ways and begin to distinguish their different roles.


For example:

In the equation 4x + 3 = 47, x is a particular unknown number.
In the formula
V = IR, V, I and R
are variable quantities, related by the formula.


Substitution

Numbers can be substitued in place of letters. This can be the case in both expressions and equations.

If a = 4

What is the value of the expression a + 2

What is the value of the expression 6a

What is the value of the expression 6a + 2


Problem Solving

Algebra can be used to solve word problems.

1. On my last birthday I weighed 125 pounds. One year later I have put on x pounds. Which expression gives my weight one year later?

a) x 125 b) 125 + x c) x - 125 d) 125x


Rearranging the Subject of Formulae

Example:-
Rearrange to find c

a = b + c To do this we need to subtract b from both sides of the equation, giving....

a - b = c

Advanced example:-
The formula for the area of a circle is A = pr2 . Solve for r in the formula .
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Formulae in Action! (Science)

  • the volume V of a cuboid of length l, breadth b and height h:

V = lbh

  • the surface area S of a cuboid with width w, depth d and height h:

S = 2dw + 2dh + 2hw

  • The voltage V in an electrical circuit, with current I and resistance R, is given by the formula:

V = IR


Speed = Distance ÷ Time
Density = Mass (g) ÷ Volume
Volume = Height x Length X Width
Force (N) = Mass(kg) x Acceleration(m/s2)
Amperes(current) = Volts ÷ Ohms(resistance)

Useful Links

General help http://www.onlinemathlearning.com/algebra-help.html
Balancing equations game http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html?open=instructions&from=topic_t_2.html